10 citations · 23 across the 9 of their papers we have counts for
10 papers
Topics in global real analytic geometry
F. Acquistapace, F. Broglia, J. F. Fernando
In the first half of twentieth century the theory of complex analytic functions and of their zerosets was fully developed. The definition of holomorphic function has a local nature…
Normalization of complex analytic spaces from a global viewpoint
Francesca Acquistapace, Fabrizio Broglia, José F. Fernando
In this work we study some algebraic and topological properties of the ring of global analytic functions of the normalization of a re…
On globally defined semianalytic sets
Francesca Acquistapace, Fabrizio Broglia, José F. Fernando
In this work we present the concept of -semianalytic subset of a real analytic manifold and more generally of a real analytic space. -semianalytic sets can be understood as t…
A global Nullstellensatz for ideals of Denjoy-Carleman functions
Francesca Acquistapace, Fabrizio Broglia, Andreea Nicoara
We prove a Nullstellensatz result for global ideals of Denjoy-Carleman functions in both finitely generated and infinitely generated cases.
Failure of the Weierstrass Preparation Theorem in quasi-analytic Denjoy-Carleman rings
Francesca Acquistapace, Fabrizio Broglia, Michail Bronshtein +2
It is shown that Denjoy-Carleman quasi-analytic rings of germs of functions in two or more variables fail to satisfy the Weierstrass Preparation Theorem. The result is proven via a…
A Nullstellensatz for Łojasiewicz ideals
Francesca Acquistapace, Fabrizio Broglia, Andreea Nicoara
For an ideal of smooth functions that is either Łojasiewicz or weakly Łojasiewicz, we give a complete characterization of the ideal of functions vanishing on its variety in terms o…
On the Nullstellensätze for Stein spaces and -analytic sets
Francesca Acquistapace, Fabrizio Broglia, Jose F. Fernando
In this work we prove the real Nullstellensatz for the ring of analytic functions on a -analytic set in terms of the saturation of Łoja…
Separation of Semialgebraic Sets
F. Acquistapace, C. Andradas, F. Broglia
In this paper we study the problem of deciding whether two disjoint semialgebraic sets of an algebraic variety over R are separable by a polynomial. For that we isolate a dense sub…
An algorithmic criterion for basicness in dimension 2
F. Acquistapace, F. Broglia, M. Pilar Velez
We give a constructive procedure to check basicness of open (or closed) semialgebraic sets in a compact, non singular, real algebraic surface . It is rather clear that if a semi…
On Brauer Groups of Real Enriques Surfaces
V. V. Nikulin, R. Sujatha
Let Y be a real Enriques surface, _2Br(Y) the subgroup of elements of order 2 of Br(Y), and s, s_{or}, and s_{nor} the number of all connected, connected orientable, and connected…